TY - JOUR
AU - Mughetti, Marco
PY - 2016/01/01
Y2 - 2024/06/18
TI - Analytic Hypoellipticity and the Treves Conjecture
JF - Bruno Pini Mathematical Analysis Seminar
JA - BPMAS
VL - 7
IS - 1
SE - Articles
DO - 10.6092/issn.2240-2829/6690
UR - https://mathematicalanalysis.unibo.it/article/view/6690
SP - 53-68
AB - We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, P, (firstly appeared and studied in [3]) having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem.
ER -